Two-variable logic with counting is decidable
Erich Grädel, Martin Otto, Eric Rosen · 2002
We prove that the satisfiability and the finite satisfiability problems for C/sup 2/ are decidable. C/sup 2/ is first-order logic with only two variables in the presence of arbitrary counting quantifiers 3/sup /spl ges/m/,m/spl ges/1. It considerably extends L/sup 2/ plain first-order with only two variables, which is known to be decidable by a result of Mortimer's. Unlike L/sup 2/, C/sup 2/ does not have the finite model property.